diff --git a/src/testing/testing.go b/src/testing/testing.go
index 216e46ee816..aa1584f2d9f 100644
--- a/src/testing/testing.go
+++ b/src/testing/testing.go
@@ -372,6 +372,7 @@ type common struct {
 	tempDirOnce sync.Once
 	tempDir     string
 	tempDirErr  error
+	tempDirSeq  int32
 }
 
 // Short reports whether the -test.short flag is set.
@@ -827,6 +828,8 @@ var tempDirReplacer struct {
 // The directory is automatically removed by Cleanup when the test and
 // all its subtests complete.
 func (c *common) TempDir() string {
+	// Use a single parent directory for all the temporary directories
+	// created by a test, each numbered sequentially.
 	c.tempDirOnce.Do(func() {
 		c.Helper()
 
@@ -849,7 +852,12 @@ func (c *common) TempDir() string {
 	if c.tempDirErr != nil {
 		c.Fatalf("TempDir: %v", c.tempDirErr)
 	}
-	return c.tempDir
+	seq := atomic.AddInt32(&c.tempDirSeq, 1)
+	dir := fmt.Sprintf("%s%c%03d", c.tempDir, os.PathSeparator, seq)
+	if err := os.Mkdir(dir, 0777); err != nil {
+		c.Fatalf("TempDir: %v", err)
+	}
+	return dir
 }
 
 // panicHanding is an argument to runCleanup.
diff --git a/src/testing/testing_test.go b/src/testing/testing_test.go
index 1340dae5c4d..dbef7066e0e 100644
--- a/src/testing/testing_test.go
+++ b/src/testing/testing_test.go
@@ -7,6 +7,7 @@ package testing_test
 import (
 	"io/ioutil"
 	"os"
+	"path/filepath"
 	"testing"
 )
 
@@ -55,8 +56,11 @@ func testTempDir(t *testing.T) {
 		t.Fatal("expected dir")
 	}
 	dir2 := t.TempDir()
-	if dir != dir2 {
-		t.Fatal("directory changed between calls")
+	if dir == dir2 {
+		t.Fatal("subsequent calls to TempDir returned the same directory")
+	}
+	if filepath.Dir(dir) != filepath.Dir(dir2) {
+		t.Fatalf("calls to TempDir do not share a parent; got %q, %q", dir, dir2)
 	}
 	dirCh <- dir
 	fi, err := os.Stat(dir)